Disk Graph 2 1 15 Inch

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1. Disk Graph 2 1 15 Inch Size
2. Disk Graph 2 1 15 Inch Celeron Laptop
3. Disk Graph 2 1 15 Inches
4. 2+1 Film
5. Disk Graph 2 1 15 Inch X

This is a complete lesson with instruction and exercises for fifth grade. It teaches students about measuring in inches, using the 1/16 parts of an inch.

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Disk Graph 2 1 15 Inch Size

1. Find the ½-inch mark, 1 ½ -inch mark, and 2 ½-inch mark on all of the rulers above.

2. Find the ¼-inch mark, the ¾-inch mark, the 1 ¼-inch mark, the 1 ¾-inch mark, the 2 ¼-inch mark,
the 2 ¾-inch mark, and the 3¼-inch mark on the bottom three rulers above.

3. On the ruler that measures in 8th parts of an inch, find and label tick marks for these points: the
1/8-inch point, the 5/8-inch point, the 7/8-inch point, the 1 5/8-inch point, and the 2 3/8-inch point.

Also, find these same points on the ruler that measures in 16th parts of an inch.

4. Look at the ruler that measures in 16th parts of an inch. On that ruler find tick marks for these points:

5. Measure the following colored lines with the rulers given. If the end of the line does not fall exactly
on a tick mark, then read the mark that is CLOSEST to the end of the line.

6. Measure the followinglines using different rulers. Cut out the rulers from the bottom of this page.

You may cut out the following rulers:

7. Find six items in your home that you can measure with your rulerand measure them.

8. Carefully measure the sides of the
quadrilateral at the right, and
find its perimeter.

9. A small rectangular bulletin board
measures 15 3/4 in. by 9 1/8 in.
What is its perimeter?

10. Janet checked the amount of sugar in 10
different cookie recipes. The amounts were (in cups):

1 1/2 1 3/8 1 1 3/4 1 1/2 1 1/8 1 1/4 1 1/4 1 1/2 3/4

a. Make a line plot from this data (below) by drawing an X-mark
for each measurement above the number line.

b. If Janet made the recipe with the least amount of sugar
three times, how much sugar would she need?

c. If Janet made the recipe with the largest amount of sugar
three times, how much sugar would she need?

11. Make a line plot from these measurements (lengths of cockroaches, in inches, in Jake's collection):

1 1/4 1 1/8 1 1/8 1 1/2 1 1 1/8 1 3/8 1 3/4 1 3/8 7/8 1 1/4 2 1/8 1/2 1 1/4 1 1/4

1 1/2 1 1/2 1 1/2 1 5/8

This time, you will need to do the scaling on the number line.

Disk Graph 2 1 15 Inch Celeron Laptop

b. What is the mode of this data set?

c. Jake took his five longest cockroaches, and placed them
end-to-end. How long a 'train' did they form?

12. Measure a bunch of pencils to the nearest 1/8 or 1/16 of an inch. Then make a line plot of
your data.

This lesson is taken from Maria Miller's book Math Mammoth Fractions 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

Math Mammoth Fractions 1

A self-teaching worktext for 5th grade that teaches fractions and their operations with visual models. The book covers fractions, mixed numbers, adding and subtracting like fractions, adding and subtracting mixed numbers, adding and subtracting unlike fractions, and comparing fractions.

Download ($3.50). Also available as a printed copy.

Learning Outcomes

• Find domain and range from a graph, and an equation.
• Give the domain and range of the toolkit functions.

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the [latex]x[/latex]-axis. The range is the set of possible output values, which are shown on the [latex]y[/latex]-axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values.

We can observe that the graph extends horizontally from [latex]-5[/latex] to the right without bound, so the domain is [latex]left[-5,infty right)[/latex]. The vertical extent of the graph is all range values [latex]5[/latex] and below, so the range is [latex]left(mathrm{-infty },5right][/latex]. Note that the domain and range are always written from smaller to larger values, or from left to right for domain, and from the bottom of the graph to the top of the graph for range.

Example: Finding Domain and Range from a Graph

Find the domain and range of the function [latex]f[/latex].

a. Make a line plot from this data (below) by drawing an X-mark
for each measurement above the number line.

b. If Janet made the recipe with the least amount of sugar
three times, how much sugar would she need?

c. If Janet made the recipe with the largest amount of sugar
three times, how much sugar would she need?

11. Make a line plot from these measurements (lengths of cockroaches, in inches, in Jake's collection):

1 1/4 1 1/8 1 1/8 1 1/2 1 1 1/8 1 3/8 1 3/4 1 3/8 7/8 1 1/4 2 1/8 1/2 1 1/4 1 1/4

1 1/2 1 1/2 1 1/2 1 5/8

This time, you will need to do the scaling on the number line.

Disk Graph 2 1 15 Inch Celeron Laptop

b. What is the mode of this data set?

c. Jake took his five longest cockroaches, and placed them
end-to-end. How long a 'train' did they form?

12. Measure a bunch of pencils to the nearest 1/8 or 1/16 of an inch. Then make a line plot of
your data.

This lesson is taken from Maria Miller's book Math Mammoth Fractions 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

Math Mammoth Fractions 1

A self-teaching worktext for 5th grade that teaches fractions and their operations with visual models. The book covers fractions, mixed numbers, adding and subtracting like fractions, adding and subtracting mixed numbers, adding and subtracting unlike fractions, and comparing fractions.

Download ($3.50). Also available as a printed copy.

Learning Outcomes

• Find domain and range from a graph, and an equation.
• Give the domain and range of the toolkit functions.

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the [latex]x[/latex]-axis. The range is the set of possible output values, which are shown on the [latex]y[/latex]-axis. Keep in mind that if the graph continues beyond the portion of the graph we can see, the domain and range may be greater than the visible values.

We can observe that the graph extends horizontally from [latex]-5[/latex] to the right without bound, so the domain is [latex]left[-5,infty right)[/latex]. The vertical extent of the graph is all range values [latex]5[/latex] and below, so the range is [latex]left(mathrm{-infty },5right][/latex]. Note that the domain and range are always written from smaller to larger values, or from left to right for domain, and from the bottom of the graph to the top of the graph for range.

Example: Finding Domain and Range from a Graph

Find the domain and range of the function [latex]f[/latex].

We can observe that the horizontal extent of the graph is –3 to 1, so the domain of [latex]f[/latex] is [latex]left(-3,1right][/latex].

The vertical extent of the graph is 0 to [latex]–4[/latex], so the range is [latex]left[-4,0right][/latex].

Example: Finding Domain and Range from a Graph of Oil Production

Disk Graph 2 1 15 Inches

Find the domain and range of the function [latex]f[/latex].

(credit: modification of work by the U.S. Energy Information Administration)

The input quantity along the horizontal axis is 'years,' which we represent with the variable [latex]t[/latex] for time. The output quantity is 'thousands of barrels of oil per day,' which we represent with the variable [latex]b[/latex] for barrels. The graph may continue to the left and right beyond what is viewed, but based on the portion of the graph that is visible, we can determine the domain as [latex]1973le tle 2008[/latex] and the range as approximately [latex]180le ble 2010[/latex].

In interval notation, the domain is [latex][1973, 2008][/latex], and the range is about [latex][180, 2010][/latex]. For the domain and the range, we approximate the smallest and largest values since they do not fall exactly on the grid lines.

Try It

Given the graph, identify the domain and range using interval notation.

Domain = [latex][1950, 2002][/latex] Range = [latex][47,000,000, 89,000,000][/latex]

Q & A

Can a function's domain and range be the same?

Yes. For example, the domain and range of the cube root function are both the set of all real numbers.

Domain and Range of Toolkit Functions

2+1 Film

We will now return to our set of toolkit functions to determine the domain and range of each.

For the constant function [latex]fleft(xright)=c[/latex], the domain consists of all real numbers; there are no restrictions on the input. The only output value is the constant [latex]c[/latex], so the range is the set [latex]left{cright}[/latex] that contains this single element. In interval notation, this is written as [latex]left[c,cright][/latex], the interval that both begins and ends with [latex]c[/latex].

For the identity function Duplicate photos fixer pro 1 8 1 download free. [latex]fleft(xright)=x[/latex], there is no restriction on [latex]x[/latex]. Both the domain and range are the set of all real numbers.

For the absolute value function [latex]fleft(xright)=|x|[/latex], there is no restriction on [latex]x[/latex]. However, because absolute value is defined as a distance from 0, the output can only be greater than or equal to 0.

For the quadratic function [latex]fleft(xright)={x}^{2}[/latex], the domain is all real numbers since the horizontal extent of the graph is the whole real number line. Because the graph does not include any negative values for the range, the range is only nonnegative real numbers.

For the cubic function [latex]fleft(xright)={x}^{3}[/latex], the domain is all real numbers because the horizontal extent of the graph is the whole real number line. The same applies to the vertical extent of the graph, so the domain and range include all real numbers.

For the reciprocal function [latex]fleft(xright)=frac{1}{x}[/latex], we cannot divide by 0, so we must exclude 0 from the domain. Further, 1 divided by any value can never be 0, so the range also will not include 0. In set-builder notation, we could also write [latex]left{x|text{ }xne 0right}[/latex], the set of all real numbers that are not zero.

Disk Graph 2 1 15 Inch X

For the reciprocal squared function [latex]fleft(xright)=frac{1}{{x}^{2}}[/latex], we cannot divide by [latex]0[/latex], so we must exclude [latex]0[/latex] from the domain. There is also no [latex]x[/latex] that can give an output of 0, so 0 is excluded from the range as well. Note that the output of this function is always positive due to the square in the denominator, so the range includes only positive numbers.

For the square root function [latex]fleft(xright)=sqrt[]{x}[/latex], we cannot take the square root of a negative real number, so the domain must be 0 or greater. The range also excludes negative numbers because the square root of a positive number [latex]x[/latex] is defined to be positive, even though the square of the negative number [latex]-sqrt{x}[/latex] also gives us [latex]x[/latex].

For the cube root function [latex]fleft(xright)=sqrt[3]{x}[/latex], the domain and range include all real numbers. Note that there is no problem taking a cube root, or any odd-integer root, of a negative number, and the resulting output is negative (it is an odd function).

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